Valentin Vladimirovich Petrov | University St. Petersburg - Rússia

• Processo: 01/13969-2
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Data de Início da vigência: 29 de abril de 2002
• Data de Término da vigência: 29 de maio de 2002
• Área do conhecimento: Ciências Exatas e da Terra - Probabilidade e Estatística
• Pesquisador responsável: Pablo Augusto Ferrari
• Beneficiário: Pablo Augusto Ferrari
• Pesquisador visitante: Valentin Vladimirovich Petrov
• Instituição do Pesquisador Visitante: Saint-Petersburg State University (SPbSU), Rússia
• Instituição Sede: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brasil
• Vinculado ao auxílio: 99/11962-9 - Fenômenos críticos em processos evolutivos e sistemas em equilíbrio, AP.TEM
• Assunto(s): Teoremas limites Intercâmbio de pesquisadores Colaboração científica
• Palavra(s)-Chave do Pesquisador: Teoremas Limite

Resumo

I plan to continue my investigations related to limit theorems of probability theory and summarized in my monograph “Limit Theorems of Probability Theory”, Oxford University Press, 1995. Special attention will be paid to strong limit theorems for sequences of independent random variables including strong laws of large numbers and laws of the iterated logarithm type. In particular, I will study broad conditions of the applicability of the classical law of the iterated logarithm and its generalizations (without any moment conditions) to sequences of independent (as well as dependent) random variables. Estimates of the growth of sums of random variables with probability 1 will be investigate. Some generalizations of the Borel–Cantelli lemma will be obtained; this lemma plays a fundamental role in proving strong limit theorems of all kinds, I hope to contribute with Brazilian researchers on these topics and on other topics proposed by them. (AU)